Are there any parks/big spaces in Makati or Taguig where kids and parents are free to run around, play ball, or Frisbee?

You could bring your family to Ayala Triangle. It is one of my personal hanging spots in Makati. I see people playing frisbee and taking advantage of its wide area. Plus, they organizes a great lights show every December which your family will surely enjoy.

Promo terbesar expert care sudah dimulai, diskon hingga Rp.100.000 sedang berlangsung di shopee, ada juga voucher diskon 100% alias gratis bagi bunda yang beruntung. Buruan cek di https://shope.ee/9UfEMMqqTg (id-10981)

You might find this link useful: https://www.tripadvisor.com.ph/Attractions-g1758900-Activities-c57-Taguig_City_Metro_Manila_Luzon.html